PI: Selim M. Shahriar / Northwestern University

1. Collaborative Research: A White Light Cavity using Anomalous Dispersion for High-Sensitivity, Broadband Operation of the Next-Generation LIGO System PI: Selim M. Shahriar / Northwestern University CoPIs: Marlan Scully / Texas A&M University Suhail Zubairy / Texas A&M University

2. PART 1: Scientific Merit of the Proposed Work

3. WHITE LIGHT CAVITY: BASIC IDEA • L=m/2 means cavity resonance • Normally,  changes with frequency • In the presence of dispersion, it is possible to change frequency • without changing . • There exists a particular variation of n as a function of so that • this compensation is exact over a large range of frequency • variation. The cavity then remains resonant over this whole range. • This is the White Light Cavity (WLC). • The cavity build-up factor remains unchanged

4. Condition for WLC: remains constant as the frequency is varied around WHITE LIGHT CAVITY: Anomalous Dispersion/Fast-Light • This simply implies an anomalous dispersion: • This happens to correspond to fast-light with infinite group velocity:

5. WHITE LIGHT CAVITY: Linewidth • WLC Linewidth is given in general by: • Ideal WLC (ng=0) has an infinite linewidth • In practice, the dispersion only linear over a finite range DIS • For ng=0, this limits the WLC linewidth to: DIS • For cavity of length L filled with a disp. med. of length l, the ideal WLC condition is

6. WHITE LIGHT CAVITY: Enhanced Sensitivity • WLC also experiences enhanced sensitivity • Consider a situation where L is changed by L away from resonance • For a regular cavity, resonance is restored by changing frequency by • a small o; the measurement of oallows measurement of L • For a generic White Light Cavity (WLC), the frequency shift • needed to restore resonance is: • For ideal WLC (ng=0), no amount of frequency shift restores resonance • In practice, the enhanced sensitivity is given by:

7. OPPOSITE EFFECT UNDER POSITIVE DISPERSION • Postive Dispersion (Slow Light) Reverses the Effects • Linewidth becomes narrower (ng>>0) : • The sensitivity to cavity length change is highly reduced:

8. |2 ,  =  - o  |1 Anomalous dispersion OBVIOUS CANDIDATE FOR WLC: Resonant Two-level System Problem: Strong absorption at line center

9. ALTERNATIVE APPROACH: Double-peak Raman Gain L.J. Wang, A. Kuzmich, and A. Dogariu, Nature, 406, 277 (2000).

10. FAST LIGHT USING ANOMALOUS DISPERSION Inside pulse delayed by: T=L/Vg-L/C=(ng-1)L/C Inside pulse advanced by: -T=(1-ng)L/C L.J. Wang, A. Kuzmich, and A. Dogariu, Nature, 406, 277 (2000).

11. OUR SCHEME FOR SLOW AND FAST LIGHT IN ONE SYSTEM 5P 3/2  Optical pump Dual-Frequency Pump Probe F=3 5S 1/2 F=2

12. ANOMALOUS DISPERSION : BASIC EXPERIMENT

13. Heterodyne Dispersion Measurement: Bi-frequency Raman Gain Note : Results showing dispersion measurement under double-gain condition for a pump frequency separation of 8 MHz. As shown in the top figure, the gain is adjusted to get a value of group index close to zero.

14. Tuning Anomalous Dispersion to Vanishing Group Index

15. Phase-sensitive detection Dispersive Medium Pump Optical pump Probe Cavity lock = medium length DISPERSIVE MEDIUM IN A RESONATOR Cavity Resonance Condition (c= o) Pos. Dispersion Neg. Dispersion

16. DISPERSIVE MEDIUM IN A RESONATOR

17. Pos. Disp.: Linewidth Narrowing and Reduced Sensitivity Experiment Simulation

18. Detuned Cavity showing Reduced Sensitivity

19. Simulation of Slow-Light Medium in a Resonator • Assumes a medium with group index ng ~ 10 • Empty cavity linewidth ~ 10 MHz; Disp. linewidth = 1 MHz

20. Frequency Shifts and Group Index Dependence

21. Simulation Experiment WLC Demonstration using Double-Gain Anomalous Dispersion

22. Effect of Group Index on WLC Broadening ng = 0.396 ng = 0.114

23. Effect of Reduced FSR of the Cavity FSR = 300 MHz FSR = 187 MHz

24. Effect of Cavity Path Length Variation: Enhanced Sensitivity

25. Effect of Cavity Path Length Variation: Enhanced Sensitivity

26. PART 2: Relevance to LIGO of the proposed work • The WLC would enhance the Sensitivity-Bandwidth Product • of the Advanced LIGO • However, the design for the Advanced LIGO is already too firmly • established for such a modification • Therefore, we believe that the WLC cavity will be relevant to the • Third-Generation LIGO.

27. BASIC FEATURES OF ADVANCED LIGO Nd:YAG Laser PRM BSM SRM DET.

28. Detector Signal • Sensitivity-Bandwidth Product is fixed by system parameters • Sensitivity is of paramount importance for Advanced LIGO design • Problem for inherently broadband and chirped sources • Several ideas have been proposed to solve this problem. These include • (i) Simply broadband dual recycling (ii) Frequency agile interferometers that • can follow a chirp, and (iii) input/output cavity techniques that can make • optimal filters for specific source spectra. Our approach seems the simplest, • and is to be compared/contrasted with these as part of this proposal Limitation of Advanced LIGO: Sensitivity-Bandwidth Product

29. Nd:YAG Laser MP BSM WLC-DE MS DET. Enhancing Sensitivity-Bandwidth Product with WLC

30. Enhancing Sensitivity-Bandwidth Product with WLC Detector Signal Without WLC Detector Signal With WLC

31. Concern: WLC needs to be demonstrated for Nd:YAG frequency • Photorefractive crystal has already been used to demonstrate Fast Light • TAMU group recently showed Slow-Light with Photorefractive crystal • We will use dual-frequency pump to create a tunable group-index anomalous • dispersion necessary for WLC suitable for LIGO, using an SPS(Sn2P2S6) crystal

32. PART 3: Capability of the proposing team to execute the proposed research

33. Project PI at Northwestern University: Selim Shahriar • Has a state-of-the-art Atomic Physics and Optics Laboratory • This laboratory is equipped with three Ti-Sapphire lasers, many diode • lasers, stable optical tables, Nd-YAG laser, optical components, • microwave components, and Sophisticated measurement tools. • Has nearly fifteen years of experiment dealing with dispersive media • Was the first to demonstrate slow-light in a solid • Was the first to demonstrate the White Light Cavity using a tunable, open • system suited for inserting in an interferometer such as LIGO

34. Project PI at Northwestern University: Selim Shahriar Five publications most relevant to the proposal: “Demonstration of a Tunable-Bandwidth White Light Interferometer using Anomalous Dispersion in Atomic Vapor,” G.S. Pati, M. Messal, K. Salit, and M.S. Shahriar, Phys. Rev. Letts. (submitted, 2006). http://arxiv.org/abs/quant-ph/0610022. “Demonstration of Tunable Displacement- Measurement-Sensitivity using Variable Group Index in a Ring Resonator,” G.S. Pati, M. Messal, K. Salit, and M.S. Shahriar, Phys. Rev. Letts. (submitted, 2006). http://arxiv.org/abs/quant-ph/0610023. “Ultrahigh Precision Rotation Sensing using a Fast-Light Enhanced Ring Laser Gyroscope ,” M.S. Shahriar, G.S. Pati, R. Tripathi, V. Gopal, and M. Messal, Phys. Rev. Letts.( submitted, 2006). http://lapt.ece.northwestern.edu/files/fast-light-enhanced-ligo “Experimental Determination of the Degree of Enhancement in Laub-Drag Augmented Rotation Sensing using Slow-Light in Sodium Vapor,” R. Tripathi, G.S. Pati, M. Messall, K. Salit and M.S. Shahriar, Optics Communications (accepted, 2006). “Controllable Anomalous Dispersion and Group Index Nulling via Bi-Frequency Raman Gain in Rb Vapor for Ultraprecision Rotation Sensing,,” G.S. Pati, R. Tripathi, M. Messall, V. Gopal, K. Salit and M.S. Shahriar, Optics Letters (submitted, 2006). http://arxiv.org/abs/quant-ph/0512260

35. Project PI at Northwestern University: Selim Shahriar Five other significant publications: “Observation of Ultraslow and Stored Light Pulses in a Solid,” A. V. Turukhin, V.S. Sudarshanam, M.S. Shahriar, J.A. Musser, B.S. Ham, and P.R. Hemmer, Phys. Rev. Lett. 88, 023602 (2002). “Long Distance, Unconditional Teleportation of Atomic States via Complete Bell State Measurements,” S. Lloyd, M.S. Shahriar, J.H. Shapiro, and P.R. Hemmer, Phys. Rev. Lett. 87, 167903 (2001). “Self-Organization, Broken Symmetry and Lasing in an Atomic Vapor: the Interdependence of Gratings and Gain,” P.R. Hemmer, M.S. Shahriar, D.P. Katz, N.P. Bigelow, L. DeSalvo, and R. Bonifacio, Phys. Rev. Letts. 77, 1468 (1996). "First Observation of Forces on Three Level Atoms in Raman Resonant Standing Wave Optical Fields," P. Hemmer, M.S. Shahriar, M. Prentiss, D. Katz, K. Berggren, J. Mervis,and N. Bigelow, Physical Review Letters, 68, 3148 (1992). "Direct Excitation of Microwave-Spin Dressed States Using a Laser Excited Resonance Raman Interaction," M.S. Shahriar and P. Hemmer, Physical Review Letters, 65, 1865(1990).

36. Texas A&M University: Marlan Scully and Suhail Zubairy • Both are world-renowned authorities in atomic and optical physics • Prof. Scully did many of the seminal work in the area of slow light • Prof. Scully was the first to propose the idea of the WLC for this • application • Have a sophisticated laboratory that will be used to perform the work • involving photorefractive crystals

37. PI at Texas A&M University: Marlan Scully Related Recent Publications: 1. A. Wicht, K. Danzmann, M. Fleischhauer, M. Scully, G. Miiller, R.H. Rinkleff, "White-light cavities, atomic phase coherence, and gravitational wave detectors", Opt. Commun. 134, 431 (1997). 2. M. O. Scully, M. S. Zubairy and M. P. Haugan, "Proposed optical test of metric gravitation theories", Phys. Rev. A 24, 2009 (1981). 3. Marlan O. Scully, “Enhancement of the Index of Refraction via Quantum Coherence”, Phys. Rev. Lett. 67, 1855 (1991). 4. W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, The Ring Laser Gyro, Rev. Mod. Phys. 57, 61 (1985). 5. M. S. Zubairy, A. B. Matsko, and M. O. Scully, "Resonant enhancement of high order optical nonlinearities based on atomic coherence", Phys. Rev. A 65, 043804 (2002). 6. M. O. Scully and M. S. Zubairy, “Playing tricks with slow light”, Science, 301, 181 (2003).

38. Five Other Significant Publications: 1. M. O. Scully and M. S. Zubairy, Quantum Optics, (Cambridge University Press, 1997), 648 pp; second printing (1999), third priniting (2001), fourth printing (2002), Chinese edition (2001), Russian translation (2003). 2. Murray Sargent III, Marlan O. Scully and Willis E. Lamb, Jr., Laser Physics, (Addison-Wesley Publishing, 1974), 432pp. 3. Marlan O. Scully and Willis E. Lamb, Jr., “Quantum Theory of an Optical Maser. I. General Theory”, Phys. Rev. 159, 208 (1967). 4. O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, “Stopping Light via Hot Atoms”, Phys. Rev. Lett., 86, 628 (2001). 5. P. R. Hemmer, A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum lithography with classical light”, Phys. Rev. Lett. 96, 163603 (2006). PI at Texas A&M University: Marlan Scully

39. PART 4: Outreach potential of the proposed work

40. Undergraduate students at NU may register for project courses as electives in partial fulfillment of their degree requirement. These courses typically involve a project that fits in with the faculty member’s research in the form of laboratory work, analysis, or computer simulation. We know personally of many instances in which this experience has prompted students’ first thoughts of pursuing a graduate degree in science. Undergraduates also will be involved in research during the summer through the Research Experience for Undergraduates (REU) program at NU, and through senior thesis and honors projects. • Efforts will be made to broaden minority student representation in science and engineering through NU programs. The university participates in the National Consortium for Graduate Degrees for Minorities in Engineering and Science (GEM) and awards fellowships to qualified students. NU also participates in the Illinois Minority Graduate Program for those students interested in teaching. NU Summer Research Opportunity Program (SROP) provides underrepresented minority sophomores and juniors majoring in the social sciences, humanities, communications, biological sciences, physical sciences, and engineering an opportunity for direct involvement in research. The program is eight weeks in length, and includes faculty-supervised research, enrichment activities that prepare undergraduates for graduate school (i.e, GRE preparation, graduate school application workshop, writing workshops, etc.). Outreach Potential at Northwestern University

41. Pathways to the Doctorate Program at Texas A&M University at College Station: The goal of the Pathways Program is to attract high achieving students within the Texas A&M University (TAMU) System to pursue careers in research and higher education. This program has established a broad range of communication channels and activities such as seminars and workshops, inter-institutional exchange programs, a mentoring program and an annual research symposium with System-wide participation. The Pathways Program enables us to contact and recruit top students from a variety of geographical, socio-economic, racial, ethnic, and cultural environments, through a partnership within the Texas A&M System that consists of nine universities, such as Prairie View A&M (a HBCU-Historically black colleges and universities), Texas A&M University - Corpus Christi (a HSI, Hispanic-serving institutions), Texas A&M University Kingsville (a HSI), and Texas A&M International University (a HSI). We expect our association with these schools through the Pathways Program to help with recruitment of students from underrepresented groups into our graduate program. • A recruiting committee regularly visits traditionally black and hispanic American institutions and participates regularly in the National Conference of Black Physics Students. These initiatives have been successful as the minority enrolment has climed up substantially. Outreach Potential at Texas A&M University